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Measuring Macroeconomic Tail Risk∗

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Measuring Macroeconomic Tail Risk∗ Measuring Macroeconomic Tail Risk∗ Roberto Marf`e† Julien P´enasse‡ This draft: July 27, 2021 Abstract This paper proposes a predictive approach to estimate macroeconomic tail risk dynamics over the long run (1876-2015). Our approach circumvents the scarcity of large macroeconomic crises by using observable predictive variables in a large international panel. This method does not require asset price information, which allows us to evaluate the empirical validity of rare disasters models. Our macro risk estimates covary with asset prices and forecast future stock returns, in line with the prediction that macroeconomic tail risk drives the equity premium. A rare disaster model, calibrated from macroeconomic data alone, further supports this interpretation. JEL: E44, G12, G17 Keywords: rare disasters, equity premium, return predictability ∗A previous version of this paper was titled \The Time-Varying Risk of Macroeconomic Disasters." We thank Daniel Andrei, Patrick Augustin, Bo Becker, Jules van Binsbergen, Pierre Collin-Dufresne, George Con- stantinides, Max Croce, Magnus Dahlquist, Darell Duffie, Leland Farmer, Xavier Gabaix, Anisha Ghosh, Eric Ghysels, Anisha Ghosh, Fran¸coisGourio, Daniel Greenwald, Robin Greenwood, Benjamin Holcblat, Hendrik H¨ulsbusch, Christian Julliard, Leonid Kogan, Peter Kondor, Christos Koulovatianos, Hening Liu, Andr´eLucas, Sydney Ludvigson, Rajnish Mehra, Christoph Meinerding, Alan Moreira, Tyler Muir, Stijn Van Nieuwerburgh, Marcus Opp, Riccardo Sabbatucci, Urszula Szczerbowicz, Adrien Verdelhan, Emil Verner, Tan Wang, Michael Weber, R¨udigerWeber, and Irina Zviadadze for helpful comments. We also benefitted from useful comments by conference and seminar participants at the Columbia University Macro Lunch, U. of Luxembourg, U. of Chile, Funda¸c~aoGet´ulioVargas (Rio), McGill University, Stockholm School of Economics, and conference participants at the CEPR ESSFM Gerzensee 2017 meeting, SAFE Asset Pricing Workshop 2017, NFA 2017, Paris December 2017 Finance Meeting, the MFA 2018, and the EFA 2020. †Collegio Carlo Alberto, Piazza Arbarello, 8, 10122 Torino, Italy; +39 (011) 670-5229; [email protected], http://robertomarfe.altervista.org/ ‡University of Luxembourg, 6, rue Richard Coudenhove-Kalergi L-1359 Luxembourg, Luxembourg; +352 466644 5824; [email protected], https://sites.google.com/view/jpenasse Many puzzles in macro-finance arise from the inability of models to reconcile, quantitatively, asset prices and macroeconomic risk. A classic example is the equity premium puzzle: averaged stock returns are far too high to be explained by the observed risk in consumption (Mehra and Prescott, 1985). Another well-known example is that valuation ratios, such as the dividend-price ratio, can forecast stock returns (Campbell and Shiller 1988b). Likewise, stock market volatility is too high to reflect forecasts of future dividends (Shiller, 1981). A potential resolution of these puzzles is that we do not observe the risk that agents genuinely care about. Rare disaster models (Rietz, 1988; Barro, 2006), in particular, posit that agents care about infrequent but severe macroeconomic crises. Gabaix(2012), Gourio(2012), and Wachter(2013) show theoretically that variation in macroeconomic tail risk can rationalize the above puzzles. Unfortunately, the success of rare disaster models relies on an elusive state variable: the time-varying probability of a large macroeconomic crisis. The apparent difficulty in measuring macroeconomic tail risk has created controversy over whether rare disaster models are falsifiable.1 In this paper, we propose a straightforward method to estimate time-varying disaster prob- abilities based on predictive regressions. Our approach does not require asset price information and can be deployed over a very long timeframe. It circumvents the scarcity of large macroe- conomic crises by exploiting the informational content of variables that forecast such crises and, in the spirit of Barro(2006), by using a broad cross-section of countries. Our measure of disaster risk allows us to document for the first time that stock prices actually respond to macroeconomic tail risk|arguably the main testable prediction of rare disaster models. Concretely, we set up a probit panel model where the left-hand-side variable is an indicator equal to one when a given country i experiences a large macroeconomic crisis in year t + 1, and zero otherwise. Our international panel builds on Barro and Urs´ua(2008) and covers 1876 to 2015, comprising 42 countries. Our baseline specification defines a macroeconomic crisis as a two-standard-deviation drop in consumption below its long-term growth path in a given year. On the right-hand side of our forecasting model, we consider a rich set of time-t predictor variables, including macroeconomic variables such as realized crises at home and abroad, but also wars, political crises, natural disasters, and (potentially) asset prices. The fitted values in this regression yield the time-t probability of a macroeconomic crisis in country i in year t + 1. Figure1 gives an overview of our main result. It shows the next-year probability of a macroeconomic crisis in the United States. The probability, which we denote byπ; ^ mostly varies between 0% and 10%, with higher levels during the Depression of 1893, the Great Depression, the two world wars, and the Great Recession of 2009. Our forecasting model performs remarkably 1For instance, John Campbell referred to the probability of rare disasters as economists' \dark matter" in his 2008 Princeton Lectures in Finance (Campbell, 2017). 1 well out-of-sample and could, therefore, be used to predict crises in real-time. The most reliable predictors include realized crises at home and in neighboring countries, wars, and the U.S. (or world) dividend-price ratio. Our macroeconomic tail risk (or macro risk, for short) estimates are remarkably insensitive to the sample period and econometric specification. Probit coefficients are broadly stable over time and between advanced and emerging countries. Changing the crisis cutoff to 1.5, 2.5, and 3 standard deviations or using the crises identified in Barro and Urs´ua (2008) also produce qualitatively similar results. Under the condition that our predictor set approximately spans the information set of eco- nomic agents,π ^ can be interpreted as the rational expectation probability of a large macroe- conomic crisis. It thus provides a benchmark with which to evaluate theories where tail risk plays a role. In the second part of the paper, we ask whether macro risk is related to the equity premium. We find that asset prices tend to be low (high dividend-price ratio) whenπ ^ is high (corr. = 0.50). By itself, the U.S. dividend-price ratio|a standard equity premium proxy in the literature (e.g., van Binsbergen and Koijen, 2010)|captures a lot of information about future crises. A one standard deviation increase in the D/P ratio raises the likelihood of a crisis by 2.1 percent, which is about half the unconditional crisis probability of 3.9%. This is precisely what one would expect if investors were shunning stocks when tail risk is high, as predicted by rare disasters models. We find similar results using the equity premium proxy proposed by Martin (2017). Furthermore, macro risk directly forecasts international stock returns, further confirm- ing the link between tail risk and the equity premium. In contrast, macro risk is only weakly related to future consumption growth, meaning that our estimates reproduce the well-known disconnect between the equity premium and consumption. Finally, these results hold when we construct macro risk excluding asset-price predictors. We next ask if rare disaster models help rationalize the equity premium puzzle and other patterns we observe in the data. Following the Mehra and Prescott(1985) approach, we calibrate the stochastic process for consumption dynamics, derive the process for prices, and compare those prices to their empirical counterparts. A benefit of our approach is that we can work with estimated consumption dynamics that exclude asset-price predictors, meaning that consumption parameters are not reverse-engineered to fit the asset pricing data. We consider a rare disaster model similar to Wachter(2013), in which agents have recur- sive preferences. Consumption growth follows an exogenous stream, which is subject to rare disasters that occur with a time-varying probability.2 The model is in discrete-time and is of 2Another strand of research maintains a constant disaster probability but assumes that the representative agent learns about the model parameters or states (e.g., Weitzman, 2007; Koulovatianos and Wieland, 2011; Du and Elkamhi, 2012; Orlik and Veldkamp, 2014; Johannes et al., 2016). Martin(2013) shows that constant disaster risk spreads across assets in a multiple-tree economy and leads to endogenous risk premia dynamics. 2 the exponential affine type so that it can be solved with standard techniques and yields simple, closed-form solutions. We use this model as a laboratory to assess both the qualitative and quantitative effects of our measure of time-varying disaster probability|that is, our model's only state variable. The model generates a high and volatile equity premium and a low risk- free rate under conservative preferences. It can also reproduce both the predictability of stock returns and the lack of predictability of consumption growth by asset prices that we observe in the data. Alternative model specifications support the idea that time-varying
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